SOLUTION: I need help on how to solve this and how to solve this with a calculator. Can someone please help me? 2.0e^(-1.5x)=1

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I need help on how to solve this and how to solve this with a calculator. Can someone please help me? 2.0e^(-1.5x)=1      Log On


   

Question 542546: I need help on how to solve this and how to solve this with a calculator. Can someone please help me?
2.0e^(-1.5x)=1
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need help on how to solve this and how to solve this with a calculator. Can someone please help me?
2.0e^(-1.5x)=1
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Calculator:
Graph
Y1 = 2*e^(-1.5x)
Y2 = 1
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Graph them on the same set of axes and find their point of intersection.
graph%28400%2C400%2C-10%2C10%2C-3%2C3%2C2e%5E%28-1.5x%29%2C1%29
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Algebraic:
e^(-1.5x) = 1/2
Take the natural log of both sides to get:
-1.5x = ln(1/2)
x = 0.4621
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Cheers,
Stan H.
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Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
2.0e%5E%28-1.5x%29+=+1 First, divide both sides by 2.
e%5E%28-1.5x%29+=+1%2F2 Substitute 1%2F2+=+0.5
e%5E%28-1.5x%29+=+0.5 Now take the natural logarithm of both sides.
ln%28e%5E%28-1.5x%29%29+=+ln%280.5%29 Apply the "power rule" to the left side.
-1.5xln%28e%29+=+ln%280.5%29 Substitute ln%28e%29+=+1
-1.5x+=+ln%280.5%29 Divide both sides by -1.5
x+=+ln%280.5%29%2F-1.5 Evaluate.
x+=+0.4621 Approx.